The dynamics of the stationary axisymmetric configuration of accreting magnetofluids surrounding a non-rotating compact object in the final stages of accretion flow is presented here. We discuss two classes of solutions for the angular momentum: a Keplerian solution, which demands no accretion flow for the fluids, and a non-Keplerian solution, which requires a radial inflow velocity for the matter. For the special case of no presence of electromagnetic fields, two sets of self-consistent analytical solutions of fully relativistic fluid equations are obtained separately for two different equations of state. The effect of the bulk viscosity coefficient on the physical functions was investigated for each state, as well as the bounds that exert on the free parameters due to last stages of the accretion-flow condition. To resolve the magnetohydrodynamical equations, we were inspired by previous sets of solutions, since the magnetofluid equations are just the same as the fluid ones in the case of vanishing electromagnetic fields. The azimuthal current in magnetofluids doesn\\\'t modify the dipolar configuration of the central object magnetic field, owing to the lack of a finite resistivity. The presence of this magnetic field doesn\\\'t affect the azimuthal velocity of the plasma, but does slow down its radial inflow, and decrease the density and pressure of the plasma. Despite the role importance of the bulk viscosity on the fluids\\\' dynamics in the absence of electromagnetic fields, exerting the magnetic field decreases this role.

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